# The probability that a man will be alive in 25 years is 3/5, and that the wife will be alive in 25 years is 2/3. What's the probability that in 25 years, both will be alive?

Jan 23, 2017

$\text{The Reqd. Prob.=} \frac{2}{5} = 0.4$

#### Explanation:

Let, $M =$the Event that a Man will be alive in $25$ years, and,

$W =$the Event that the (Man's) Wife (!) will be alive in $25$ years.

We are said that, $P \left(M\right) = \frac{3}{5} , \mathmr{and} , P \left(W\right) = \frac{2}{3}$.

We require $P \left(M \cap W\right)$

Observe that, $M \mathmr{and} W$ are Independent Events , so that,

$P \left(M \cap W\right) = P \left(M\right) P \left(W\right)$. Hence,

$\text{The Reqd. Prob.=} \left(\frac{3}{5}\right) \left(\frac{2}{3}\right) = \frac{2}{5} = 0.4$

Enjoy Maths.!